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Do the lectures specify at any point the definition of a 'Differentiable function'? The concept was used in a example and a recitation session..
 2 years ago
 2 years ago
Do the lectures specify at any point the definition of a 'Differentiable function'? The concept was used in a example and a recitation session..
 2 years ago
 2 years ago

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ac7qzBest ResponseYou've already chosen the best response.0
A "differentiable function" is one which is continuous over all the values of x you're interested in, and its derivative is also continuous. This means there are no sharp corners in the original function, only smooth transitions.
 2 years ago

TebelloBest ResponseYou've already chosen the best response.1
Differentiation is defined by a limit, and limits need not always exist. If the limit \[\lim_{h \rightarrow 0} \frac{f(x+h)  f(x)}{h}\] exists at a particular x value then we say the function is differentiable at that point. It it exists for all x in an interval then it is differentiable on that interval. Note that the limit is double sided, so implicit in this definition is the fact that no function defined on a closed interval can be differentiable on that closed interval, thus why the wording of many of the basic theorems insist on certain intervals being open...
 2 years ago
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